Microfluidic mixer having channel width variation for enhanced fluid mixing

ABSTRACT

A micromixing apparatus includes a mixing microchannel formed in a top surface of a substrate having a channel length and a variable channel width defined by a first sidewall surface and an opposing second sidewall surface. The channel width varies from a minimum channel width h to a maximum channel width H in a ratio of H:h≧1.1:1.0. A first inlet is for injecting a first fluid into the mixing microchannel and a second inlet for injecting a second fluid into the mixing microchannel. The first and second fluid flow in a flow direction in the mixing microchannel along the channel length. The first sidewall surface includes first curved surface portions and the second sidewall surface includes a second curved surface portions. The plurality of first curved surface portions and plurality of second curved surface portions are non-overlapping to provide the variable channel width.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of Provisional Application Ser. No.61/094,529 entitled “Microfluidic Mixer”, filed Sep. 5, 2008, which isherein incorporated by reference in its entirety.

U.S. GOVERNMENT RIGHTS

The U.S. Government has rights to embodiments of this invention based onNational Science Foundation grant ECS-0348603.

FIELD

Disclosed embodiments relate to micro-mixing apparatus having passivefeatures for generating enhanced fluid mixing of miscible fluid streams.

BACKGROUND

Fluid mixing is a key operation for a variety of processes. For example,fluid mixing is an important unit operation for lab-on-a-chip (LOC)bio-analysis system where often quick and efficient mixing of reactantsis required. In the case of a microfluidic mixer, the mixer has toprovide a sufficiently mixed solution in a confined length of themicro-device, such as before the point where detection is taking place.

Fluidic devices made by MicroElectroMechanicSystem (MEMS) technology aregenerally termed microfluidics, which have channel dimensions rangingfrom microns to a few millimeters. Since it is possible to perform microfabrication with high accuracy and low cost due to the development oflithography-based processing, microfluidic devices such as mixingapparatus (micro mixer), chemical reactors (micro reactor), micro TAS(Total Analysis System: LOC) and microchemistry plants are all known.

Mixing in microfluidic devices can be provided by active mixing systemsor passive mixing systems. Active mixing systems utilize one or morepowered sources to enhance mixing, such as vibrational sources to inducevibration in the microchannel. The need to supply power and itsassociated powered source adds to the cost, complexity and usefulness incertain mixing applications.

Passive systems provide a versatile solution to simplify the design andfabrication of microfluidic devices, and are highly compatible withcurrent microfabrication techniques. Hence, passive mixing systemsprovide a cost-effective mixing solution. In a conventional T-mixer orY-mixer, 2 microchannels having a small channel width (e.g., 50-100 μm)are merged into a single microchannel (e.g. 100 μm channel width) inwhich mixing takes place. Due to the small dimensions of themicrochannels, fluid flow is generally highly laminar and mass transportin the mixing channel occurs only by diffusion, normal to the flowdirection. To improve mixing, passive mixing systems can include shapingof the mixing microchannel (e.g., a serpentine or wavy constant widthmicrochannel), or flow obstacles within the mixing microchannel.

SUMMARY

This Summary is provided to comply with 37 C.F.R. §1.73, presenting asummary of the invention to briefly indicate the nature and substance ofthe invention. It is submitted with the understanding that it will notbe used to interpret or limit the scope or meaning of the claims.

Embodiments of the invention describe passive micromixing apparatus thatprovide improved mixing efficiency. The Inventors have recognized thatthe diffusive mass flux between two miscible fluid streams flowing in agenerally laminar manner in a mixing microchannel is enhanced if thevelocity at their diffusion interfaces are increased. Based on thisrecognition, an in-plane passive micromixing concept is described hereinfor use in various fluid mixing apparatus.

The micromixing apparatus have opposing sidewalls that include out ofphase curved surface portions that thus provide a variable microchannelwidth along the length of the mixing microchannel. The variablemicrochannel width is such that the maximum of the flow velocity profilecoincides with the transversely progressing (outwardly from thecenterline) diffusion fronts repeatedly (i.e. a plurality of times)throughout the length of the mixing microchannel. The varying isgenerally periodic varying. Such arrangements increase the velocity atthe diffusion interface between the fluids which has been found by theinventors to enhances the diffusive mass flux between the two fluidstreams flowing in the microchannel, and thus enhance mixing.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a depiction of Species A diffusing into liquid film Bflowing with a given velocity profile, provided to aid in understandingof certain theoretical aspects of embodiments of the invention.

FIG. 2 shows a top view depiction of an exemplary micromixing apparatus,according to an embodiment of the invention.

FIG. 3 shows an evaluation of mixing performance obtained from anexemplary micromixing apparatus according to an embodiment of theinvention using color changes as a result of the mixing of a pHindicator (phenolphthalein) and a basic solution (sodium hydroxide,pH=12.5).

FIG. 4A shows mixing performance obtained from an exemplary micromixingapparatus according to an embodiment of the invention at a given mixinglength (L=8 mm) as a function of flow Reynolds number (Re), while FIG.4B shows mixing performance at a given flow rate (Q=1000 μl/hr, Re=0.91)as a function of mixing length, according to an embodiment of theinvention.

FIG. 5 shows a micro particle image velocimetry measurement obtainedfrom an exemplary micromixing apparatus according to an embodiment ofthe invention that is seen to be primarily a laminar flow.

DETAILED DESCRIPTION

Disclosed embodiments are described with reference to the attachedfigures, wherein like reference numerals are used throughout the figuresto designate similar or equivalent elements. The figures are not drawnto scale and they are provided merely to illustrate the disclosedembodiments. Several aspects are described below with reference toexample applications for illustration. It should be understood thatnumerous specific details, relationships, and methods are set forth toprovide a full understanding of the disclosed embodiments. One havingordinary skill in the relevant art, however, will readily recognize thatthe disclosed embodiments can be practiced without one or more of thespecific details or with other methods. In other instances, well-knownstructures or operations are not shown in detail to avoid obscuring thedisclosed embodiments. The disclosed embodiments are not limited by theillustrated ordering of acts or events, as some acts may occur indifferent orders and/or concurrently with other acts or events.Furthermore, not all illustrated acts or events are required toimplement a methodology in accordance with disclosed embodiments.

As described above, the Inventors have recognized that the diffusivemass flux between two miscible fluid streams flowing laminar in amicrochannel is significantly enhanced if the velocity at theirdiffusion interfaces are increased. The effect of velocity on diffusionacross an interface is described from a theoretical basis below.Although the theory presented herein is believed to be accurate,embodiments of the invention may be practiced independent of the theoryunderpinning the mixing efficiency evidenced in the Examples providedherein by micromixing apparatus according to embodiments of theinvention.

FIG. 1 is a depiction of Species A from a constant source showndiffusing in the z-direction into a liquid film B, flowing with a givenvelocity profile, provided to aid in understanding certain theoreticalaspects of embodiments of the invention. The simplified transport(differential) equation for describing the concentration of Species A infilm B, c_(A), can be written as follows with D_(A,B) being the binarydiffusion constant, where the maximum velocity of Species B at theinterface is v_(max).

$\begin{matrix}{{v_{\max}\frac{\partial c_{A}}{\partial z}} = {D_{A,B}\frac{\partial^{2}c_{A}}{\partial x^{2}}}} & (1)\end{matrix}$

The boundary conditions are: c_(A)=0 (at z=0), c_(A)=c_(0A) (at x=0),and ∂c_(A)/∂x=0 (x=δ). Using a similarity variable approach, thesolution to (1) has the following form:

$\begin{matrix}{\frac{c_{A}}{c_{0A}} = {{1 - {\frac{2}{\sqrt{\pi}}{\int_{0}^{x/\sqrt{4D_{A,B}{z/v_{\max}}}}{{\exp( {- \xi^{2}} )}\ {\mathbb{d}\xi}}}}} = {{erfc}( \frac{x}{\sqrt{4D_{A,B}{z/v_{\max}}}} )}}} & (2)\end{matrix}$The local mass flux of Species A at the interface may be found asfollows:

$\begin{matrix}{{N_{A,x,{interface}}\mspace{11mu}(z)} = {{{- D_{A,B}}\frac{\partial c_{A}}{\partial x}} =_{x = 0}{c_{0A}\sqrt{\frac{D_{A,B}v_{\max}}{\pi\; z}}}}} & (3)\end{matrix}$It is observed from (3) above that increasing the magnitude of thevelocity at the interface (v_(max)) translates into enhancement of thediffusive mass flux across the interface.

Mixing is now considered where two miscible liquids flow side by side ina laminar flow regime, so that a diffusion front for each fluid (thus 2diffusion fronts and as a result 2 interfaces) would be developed. Thesediffusion fronts progress in the transverse direction (i.e. away fromthe centerline of the microchannel) as one moves downstream in themicrochannel. Based on Einstein's relationship for Brownian motion, theposition of the diffusion fronts/interfaces progresses in the transversedirection (relative to the flow direction) as follows:

$\begin{matrix}{{x^{\prime}(z)} = {( {2D_{A,B}\tau} )^{\frac{1}{2}} = ( {2D_{A,B}\frac{z}{U}} )^{\frac{1}{2}}}} & (4)\end{matrix}$where x′, τ and U are displacement of the interface from the centerlineof the microchannel, channel residence time and average fluid velocity,respectively. The Inventors have recognized the following that are usedin embodiments of the invention:(i) The mass flux at the diffusion interfaces between two species isenhanced as the interface velocity is increased; and(ii) The respective diffusion interfaces both progress transverse to thedirection of the fluid flow (away from the centerline of the mixingmicrochannel) as one moves downstream through the mixing microchannel.

Based on (i) and (ii), passive mixing apparatus are described hereinthat perform enhanced mixing based on flow profile variation along thelength of the microchannel. This flow profile variation is due to thesidewall designs described herein in the mixing microchannel that causesthe maximum of the velocity profile, v_(z-max), to be shifted or, rather“swept” in the transverse direction (to the flow direction) as one movesdownstream through the mixing microchannel such that v_(z-max) overlapsthe transversely progressing diffusion interfaces (fronts) repeatedlyover the length of the mixing microchannel.

With respect to (i), the overall mass flux at the interfaces wouldincrease due to higher velocities. This is in contrast with theconventional T or Y mixer that has a constant parabolic velocityprofile, where the maximum of the velocity profile is fixed at thecenterline along the entire length of the mixing microchannel.Accordingly, for a conventional T or Y mixer, as the diffusion frontsmove out transversely away from the centerline as one moves downstreamthrough the mixing microchannel, the respective diffusion fronts bothcoincide with the slower moving lamellae of fluid. Lower diffusioninterface-velocities result in rapid reduction of the diffusive flux andhence poor mixing performance provided by the conventional T or Y mixer.

FIG. 2 shows a top view depiction of an exemplary micromixing apparatus100, according to an embodiment of the invention. Micromixing apparatus100 comprises a substrate 105 having a top surface 106. Substrate 105can comprise a variety of materials including an inorganic material(e.g., silicon, glass, quartz), an organic material (e.g.,polycarbonate, polymethamethylacrylate, polydimethylsiloxane, cyclicolefin copolymer) or a metallic material (e.g. aluminum, titanium, ironalloys).

Micromixing apparatus 100 comprises a microchannel 110. Microchannel 110can be formed from processing the top surface 106 of substrate 105 usinga laser ablation process, such as with a polymer substrate using asingle masking level. Another fabrication option comprisesphotolithography followed by a replication molding process in which amaster template is made by photolithography and the final product ismolded, imprinted or casted over the master template. However, thefabrication method for the master template is not restricted tophotolithography. Conventional machining or electroplating procedurescan also be used. Another fabrication alternative comprises a chemicaletch process, such as in the case of a silicon substrate.

Yet another fabrication method can be used that is commonly referred toas “soft lithography”. In this process, a photosensitive (PR) material(e.g., SU-8) is spin coated on the surface of a polished wafer, such asa silicon wafer. Micromixer features are transferred from a mask on thePR via conventional photo-lithography techniques. The developed patternsserve as a mold. Liquid polymer mixed with a curing agent is poured onthe mold and allowed to cure at room temperature; taking the shape ofthe mold. The features will be cast on to the polymer generating openmicrocanals. Eventually, the layer with the features is peeled off theoriginal surface and bonded to another blank layer of polymer or a glassslip forming closed microchannels. As known in the art, siliconsubstrates have the advantage of being able to form electronic deviceson the same substrate (i.e. chip) as the micromixing apparatus 100.

Although not shown in FIG. 2, micromixing apparatus 100 generallycomprises a packaged micromixing apparatus provided by adding a laminatelayer, such as formed from a lamination process. For example, a thin PETfoil coated with a melting adhesive film layer can be pressed by aheated lamination roller onto the surface 106 of the substrate 105 toprovide a lid. The lid of the packaged micromixing apparatus willprovide a planar top surface for the apparatus.

A first inlet 121 is for injecting a first fluid (liquid or gas) intothe microchannel 110 and a second inlet 122 is for injecting a secondfluid (liquid or gas) into the microchannel 110. The first and secondfluid species are generally different in chemical composition. The firstand second fluid flow in a flow direction (the x-direction shown in FIG.2) along the length of the microchannel 110.

As shown in FIG. 2, the parameters a and b define the shape of theellipsoid used to generate the sidewall patterns for first sidewallsurface 110(a) and second sidewall surface 110(b) of microchannel 110.Although first sidewall surface 110(a) and second sidewall surface110(b) are shown as minor images of one another, being offset in theflow direction by the parameter g shown in FIG. 2, embodiments of theinvention are not limited to first sidewall surface 110(a) and secondsidewall surface 110(b) being mirror images of one another. Othersidewall feature shapes can be generated using trigonometric functions(sin, cosine) which repeat on either side of the microchannel with aphase lag, such that the arrangement expands and contracts the flowprofile non-symmetrically. Moreover, although both first sidewallsurface 110(a) and second sidewall surface 110(b) include both straightwall and curved wall portions, in another embodiment first sidewallsurface 110(a) and second sidewall surface 110(b) include curved wallportions throughout.

As shown in FIG. 2, the microchannel 110 has a channel width defined bythe distance between opposing first sidewall surface 110(a) and secondsidewall surface 110(b) which is seen to change along the length of themicrochannel 110 and is thus referred to as a variable channel width.The channel width is in the direction perpendicular to the flowdirection (the x-direction shown in FIG. 2), and thus is the y-directionin FIG. 2. The variable channel width is seen to vary between a minimumchannel width h and a maximum channel width H.

As shown in FIG. 2, λ is the periodic length between repeating sidewallprofiles and the parameter g represents the lag between the respectivesidewall profiles on opposing sides of the microchannel 110. If theparameter g becomes too short or too long, keeping other parametersconstant, sidewall interference and parallel opposing walls, generallyresult. The parameter g shown in FIG. 2 varies within the period λ inits magnitude, and is typically 0.4λ<g<1.6λ.

The first sidewall surface 110(a) includes plurality of first curvedsurface portions 116 and the second sidewall surface 110(b) includesplurality of second curved surface portions 117. The first curvedsurface portions 116 and second curved surface portions 117 are seen tobe non-overlapping (not opposing one another) being offset by theparameter g so that the channel width varies along the length of themicrochannel 110.

In the case a=b, the ellipsoid becomes a circle. The parameters a and bare chosen so that the sidewall shapes expand or contract the width ofthe microchannel asymmetrically with respect to the center line of themicrochannel. The ellipse parameters a and b aid in defining how steeplyeach of the sidewalls contracts or expands. Although the respectivecurved surface portions 116 and 117 shown in FIG. 2 are shaped asellipsoidal arcs, curved surface portions 116 and 117 can comprise othercurved shapes, such as circular arcs.

The ratio of H:h quantifies the maximum degree of variation in channelwidth along the length of the microchannel 110. The ratio of H:his≧1.1:1.0 such as 2:1 to 8:1, and is typically 3:1 to 5:1. Sharpcorners can be removed by smoothening the walls using known methods suchas the Bezier curve to ensure that no dead volume regions are created inthe micromixing apparatus 100. In one embodiment, numerical simulationsusing ANSYS® software for two-dimensional numerical simulations usingthe FLOTRAN® module of ANSYS® to solve the laminar flow and multiplespecies equations result in values of H=200, h=50, a=300, b=100, R=100,λ=400 and g=200 with microchannel depth of 100 (units all μm) to achievemaximum mixing efficiency. The actual devices were built based on thesimulation results. In terms of λ, the total length mixer length of themicrochannel 110 was 50λ.

Microchannel 110 shown in FIG. 2 has optional periodicity in the firstsidewall surface 110(a) and the second sidewall surface 110(b) so thatthe channel width varies periodically along the length of themicrochannel 110. More specifically, the first curved surface portions116 of the first sidewall surface 110(a) and the second curved surfaceportions 117 of the second sidewall surface 110(b) both repeatperiodically with wavelength λ along the channel length and thus have aconstant spacing in the flow direction (the x-direction shown in FIG.2).

In operation of micromixing apparatus 100 as shown in FIG. 2, thevelocity profile (in flow direction, i.e. the x-direction) variesthroughout the length of the microchannel 110 periodically due to theprofile of the curved surface portions 116 and 117. Such an arrangementresults in the maximum velocity value along the flow direction of thefluids shifting from the center and sweeping in the transverse directionperiodically along the length of the microchannel 110, overlapping theprogressing diffusion fronts, thus enhancing the diffusion to improvemixing of the first and second fluids. Accordingly, the maximum fluidvelocity is generally away from the center of the width of themicrochannel, and instead moves (changes) along the length of themicrochannel 110 from being within the second fluid in position 131(maximum fluid velocity=longest arrow) up to reach the first fluid (thuspassing through the center of the width just briefly) in position 132(maximum fluid velocity=longest arrow), then back to the first fluid,etc.

Micromixing apparatus described herein have several significantadvantages as compared to conventional micromixing apparatus. Suchmixing apparatus are planar and does not have complex 3D features. Thissimplifies fabrication and reduces fabrication expense. As describedabove, one step lithography can be used for the mold and replication ofmicromixing apparatus in polymer materials can be accomplishedrepeatedly over the life of the mold. In addition, the micromixingapparatus are passive, therefore only the fluids need to be pumped inand there are no additional complications. Moreover, micromixingapparatus described can be used as a standalone or integrated in amicrofluidic platform. Furthermore, the function of the mixer is wellsuited for low flow rate applications encountered in majority ofmicrofluidic applications.

Embodiments of the invention can be used in a variety of microfluidicdevice types. For example, a mixing apparatus (micro mixer) as describedabove, a chemistry reactor (micro reactor), a micro TAS LOC system and amicrochemistry plant. Other exemplary applications include, but are notlimited to, other technologies, including pressure sensors and medicaldiagnostic systems.

Examples

Embodiments of the invention are further illustrated by the followingspecific Examples, which should not be construed as limiting the scopeor content of embodiments of the invention in any way.

A typical procedure for fabricating microchannels for micromixingapparatus referred to as “soft lithography” is described below. A layerphotoresist (SU8 Microchem®, MA) is spin coated on a polished substrate.The thickness of the coating based on spinning speed would determine theheight of the microchannels (15 seconds @ 500 rpm followed by 45 seconds@ 1,000 rpm). The soft-bake process includes two stages (10 minutes @70° C. followed by 30 minutes @ 105° C. on a hotplate). SU-8 is ahigh-contrast, epoxy based negative photoresist used for micromachiningand other microelectronic and microfluidic applications, where thick,chemically and thermally stable features are desired. The next step ispatterning via photolithography. SU-8 is optimized for near UV (350-400nm) exposure (EVG 620 Mask Aligner, NY). The optimal exposure dosedepends on film thickness (thicker films require higher dosage) andprocess parameters (total dosage for targeted thickness is within350-400 mJ/cm²). The UV-light exposed and subsequently thermallycross-linked portions of the film are rendered insoluble to liquiddevelopers. SU-8 is used to create high aspect ratio structures withnear vertical walls in very thick films due to its optical properties.

Post exposure bake is done directly after exposure in two steps (3minutes @ 75° C. followed by 10 minutes @ 105° C.). After cooling theSU-8 developer (MICROCHEM®, MA) is used for developing the patterns. Thefabricated SU-8 mold will be used to replicate patterns in theelastomeric resin. Patterns can be replicated as many times, dependingon the quality of the mold. Sylgard 184 Silicone® (Dow Corning, MI) isused for fabricating the microchannels. The elastomer is mixed with thecuring agent and poured on the mold and allowed to cure eventuallytaking the shape of the patterned micro-canals. The layer consisting oftransferred patterns is bonded to another blank layer of PDMS or glassslide to create a closed fluidic channel by surface treatment (Coronatreatment). Inlet and outlet ports are punched in the blank layers priorto bonding.

FIG. 3 shows an evaluation of mixing performance obtained from anexemplary micromixing apparatus according to an embodiment of theinvention using color changes as a result of mixing of a pH indicator(phenolphthalein 1%, isopropyl alcohol 60%, water balance) and a basicsolution (1.6% sodium hydroxide, pH=12.5). The two colorless solutionswere introduced at the inlets of the devices by an infusion pump. Whenmixed, a pink/purple region was created which expands transversely withtwo interfaces away from the centerline of the microchannel as thesolutions further mix downstream as shown in FIG. 3. Color images atselect cross sections were converted into thresholded grayscale images.Dark pixels, gray intensity I=0, show fully mixed regions whereas brightpixels, I=1, are non-mixed portions of the flow. Standard deviation ofgray intensity around the darkest gray pixel (completely mixed region inthe middle of the channel) is calculated for the pixels of the selectedcross section.

$\begin{matrix}{\sigma = \lbrack {\frac{1}{n}{\sum\limits_{i = 1}^{n}\;( {I_{\min} - I_{i}} )^{2}}} \rbrack^{\frac{1}{2}}} & (5)\end{matrix}$n is the number of the cross section pixels, I_(i) is gray intensity ofpixel i of the selected cross section and I_(min) is the minimum grayintensity. When there is no mixing, the standard deviation, σ=1, andideally at full mixing it will reach 0 as all pixels attain uniform grayintensity. The level of mixing (percentage) is defined as follows:M=(1−σ)×100  (6)

FIG. 4A shows mixing performance obtained from an exemplary micromixingapparatus according to an embodiment of the invention at a given mixinglength (L=8 mm) as a function of flow Reynolds number (Re), while FIG.4( b) shows mixing performance at a given flow rate (Q=1,000 μl/hr,Re=0.91) as a function of mixing length. The mixing performance wasevaluated in comparison to the T mixer and the Tesla mixer as a functionof flow Reynolds number and mixing length. The results obtainedevidences the effectiveness of the passive micromixing concept andsignificant improvement of mixing performance over existing passivemicro-mixer designs.

FIG. 5 shows micro particle image velocimetry (μPIV) measurement of aprimarily laminar flow obtained from an exemplary micromixing apparatusaccording to an embodiment of the invention. The bottom layers as shownare seen to move faster than the top layers at the section identified as“A”, whereas in the section identified as “B” the situation is reversedso that the top layers move faster than the bottom layers confirmingvariation of the velocity profile. The maximum of the velocity profilesweeps across the transverse direction, repeatedly, overlapping theprogressing diffusion fronts throughout the length of the mixingmicrochannel.

While various embodiments of the invention have been described above, itshould be understood that they have been presented by way of exampleonly, and not limitation. Numerous changes to the disclosed embodimentscan be made in accordance with the disclosure herein without departingfrom the spirit or scope of the disclosed embodiments. For example,embodiments of the invention can also include powered sources to furtherenhance fluid mixing, such as vibrational sources to induce vibration inthe microchannel. Thus, the breadth and scope of embodiments of theinvention should not be limited by any of the above explicitly describedembodiments. Rather, the scope of the invention should be defined inaccordance with the following claims and their equivalents.

Although the embodiments of invention have been illustrated anddescribed with respect to one or more implementations, equivalentalterations and modifications will occur to others skilled in the artupon the reading and understanding of this specification and the annexeddrawings. In addition, while a particular feature may have beendisclosed with respect to only one of several implementations, suchfeature may be combined with one or more other features of the otherimplementations as may be desired and advantageous for any given orparticular application.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting to embodiments ofthe invention. As used herein, the singular forms “a,” “an,” and “the”are intended to include the plural forms as well, unless the contextclearly indicates otherwise. Furthermore, to the extent that the terms“including,” “includes,” “having,” “has,” “with,” or variants thereofare used in either the detailed description and/or the claims, suchterms are intended to be inclusive in a manner similar to the term“comprising.”

Unless otherwise defined, all terms (including technical and scientificterms) used herein have the same meaning as commonly understood by oneof ordinary skill in the art to which embodiments of the inventionbelongs. It will be further understood that terms, such as those definedin commonly used dictionaries, should be interpreted as having a meaningthat is consistent with their meaning in the context of the relevant artand will not be interpreted in an idealized or overly formal senseunless expressly so defined herein.

The Abstract of the Disclosure is provided to comply with 37 C.F.R.§1.72(b), requiring an abstract that will allow the reader to quicklyascertain the nature of the technical disclosure. It is submitted withthe understanding that it will not be used to interpret or limit thescope or meaning of the following claims.

The invention claimed is:
 1. A micromixing apparatus, comprising: asubstrate having a top surface; a mixing microchannel formed in said topsurface of said substrate having a channel length and a continuouslyvariable channel width along said channel length defined by a firstsidewall surface and an opposing second sidewall surface, wherein saidcontinuously variable channel width continuously varies from a minimumchannel width h to a maximum channel width H in a ratio of H:h≧1.1:1.0,and a first inlet for injecting a first fluid into said mixingmicrochannel and a second inlet for injecting a second fluid into saidmixing microchannel, wherein said first and said second fluid flow in aflow direction in said mixing microchannel along said channel length,and wherein said first sidewall surface includes a plurality of firstcurved surface portions and said second sidewall surface includes aplurality of second curved surface portions, said plurality of firstcurved surface portions and said plurality of second curved surfaceportions non-overlapping by being offset with respect to one anotheralong said channel length to provide said continuously variable channelwidth.
 2. The micromixing apparatus of claim 1, wherein said pluralityof first curved surface portions of said first sidewall surface and saidplurality of second curved surface portions of said second sidewallsurface both repeat periodically along said channel length and have aconstant spacing in said flow direction between respective ones of saidplurality of first curved surface portions and said plurality of secondcurved surface portions.
 3. The micromixing apparatus of claim 1,wherein said plurality of first curved surface portions and saidplurality of second curved surface portions are ellipsoidal arc shaped.4. The micromixing apparatus of claim 3, wherein said first sidewallsurface and said second sidewall surface are minor images of one anotherwith a lateral offset in said flow direction.
 5. The micromixingapparatus of claim 4, wherein a periodic length between repeating onesof said plurality of first curved surface portions and said plurality ofsecond curved surface portions is λ and g represents a lag between therespective ones of said plurality of first curved surface portions andsaid plurality of second curved surface portions on opposing sides ofsaid microchannel, and wherein 0.4λ<g<1.6λ.
 6. The micromixing apparatusof claim 4, wherein said lateral offset in said flow direction is 50 to500 μm.
 7. The micromixing apparatus of claim 1, wherein said ratio ofH:h is from 2:1 to 8:1.
 8. The micromixing apparatus of claim 1, whereinsaid substrate comprises a polymer.
 9. The micromixing apparatus ofclaim 1, wherein said first sidewall surface and said second sidewallsurface include both straight wall portions and curved wall portions.